The typical FFF item gives an example of a mathematical argument that is wrong but tricky. Sometimes the problem is that the argument, while visibly (even extravagantly) incorrect, gives the right answer. Other times, the argument contains a subtle error, or uses a method that is correct for unexpected reasons.

For example, here’s a method (section 1.4) for adding two fractions with the same single-digit denominator and single-digit numerators, such as 5/8 and 1/8. First you juxtapose the two denominators to get 88. Then you juxtapose the numerators, getting 51, but of course addition is commutative, so you should also juxtapose them in the other order, getting 15. So